Electrical conductivity of a monolayer produced by random sequential adsorption of lineark-mers onto a square lattice

Abstract

The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent adsorption sites) onto a square lattice was studied by means of computer simulation. Overlapping with pre-deposited k-mers and detachment from the surface were forbidden. The RSA process continued until the saturation jamming limit, pj. The isotropic (equiprobable orientations of k-mers along x and y axes) and anisotropic (all kmers aligned along the y axis) depositions for two different models: of an insulating substrate and conducting k-mers (C-model) and of a conducting substrate and insulating k-mers (I-model) were examined. The Frank-Lobb algorithm was applied to calculate the electrical conductivity in both the x and y directions for different lengths (k = 1 -128) and concentrations (p = 0 -pj) of the k-mers. The 'intrinsic electrical conductivity' and concentration dependence of the relative electrical conductivity Σ(p) (Σ = σ/σm for the C-model and Σ = σm/σ for the I-model, where σm is the electrical conductivity of substrate) in different directions were analyzed. At large values of k the Σ(p) curves became very similar and they almost coincided at k = 128. Moreover, for both models the greater the length of the k-mers the smoother the functions Σxy(p), Σx(p) and Σy(p). For the more practically important C-model, the other interesting findings are (i) for large values of k (k = 64, 128), the values of Σxy and Σy increase rapidly with the initial increase of p from 0 to 0.1; (ii) for k ≥ 16, all the Σxy(p) and Σx(p) curves intersect with each other at the same iso-conductivity points; (iii) for anisotropic deposition, the percolation concentrations are the same in the x and y directions, whereas, at the percolation point the greater the length of the k-mers the larger the anisotropy of the electrical conductivity, i.e., the ratio σy/σx (> 1).

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

“…The multi-scale percolation behavior of the effective conductivity has been studied using a lattice model [27,28]. A lattice approach has also been applied to study the electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of non-overlapping conductive rodlike particles onto an insulating substrate [29].…”

Simulation of the electrical conductivity of two-dimensional films with aligned rod-like conductive fillers: Effect of the filler length dispersity

“…Due to anisotropic deposition of the rods according to the given value of the order parameter s, the electrical conductivity of the film may be different in two mutually perpendicular directions. To characterize such an electrical anisotropy, we used the quantity 30,31 δ = log 10 σ /σ ⊥ log 10 ∆ . (14) Note that, at the percolation threshold, the effective electrical conductivity of a two-phase thin film at equal concentrations of the phases and with a random distribution of them is equal to the geometric mean of the conductivity of the phases…”

“…Recently, simulations of the electrical conductivity of two-dimensional (2D) systems with rod-like fillers of equal length have been performed both in lattice [30][31][32] and in continuous 33,34 approaches. In the present work, we have examined the effect of dispersity of filler length on the electrical conductivity of 2D composites with aligned rod-like fillers by means of computer simulation.…”

Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear k-mers onto a square lattice

“…This RRN is an image of the original monolayer, it has a regular structure but randomly distributed conductivities. A preliminary scaling analysis of the electrical conductivity behaviour at different values of k and L has recently been performed for the defect-free problem [20]. The difference between the approximated value of electrical conductivity in the limit of the infinite system and L = 100k was of the order of several percent.…”

“…This region corresponds to a monolayer with a high electrical conductivity along the y direction and a low electrical conductivity along the x direction. For characterization of the electrical anisotropy of monolayers, we used the same quantity as in [20] …”